1) 2x+7x=
2) 8b-5b=
3) 5m+2m-4m=
4) a+a+a+a+a=
5) 2x+3x+6x-4x=
6) 2a+2b+a+3b=
7) 2x+7x-4=
8) 2m-2b-m+4b=
9) 10a+2b+2c+3a-b+4c=
10) 5+2 b-4+7 b=
11) 9 p+3 q-2 p-3 q=
12) a+2 b+a-b-10=

Answer:

7h+1=29 is equal to 7 x 4 + 1=29

Step-by-step explanation:

We know that 7 times 4 = 28. So the value of h is 4. And of course, you add the one.

9514 1404 393

Answer:

  8.  50 yards

  9.  9%

Step-by-step explanation:

In each case, we fill in the given values in the formula, then divide both sides of the equation by the coefficient of the variable.

The missing formula is ...

  A = LW . . . . where A is area, L is length, W is width

  6000 yd² = (120 yd)W

  W = (6000 yd²)/(120 yd) = 50 yd . . . the width of the field

__

The missing formula is ...

  I = Prt . . . . where I is the interest on principal P at rate r for t years

  1800 = 5000(r)(4)

  r = 1800/20000 = 0.09 = 9% . . . interest rate on the investment

Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

For p(x<62) and p(x>68), we can use the z-score formula to calculate the probability.

p(x<62), the z-score formula is (62-64)/18 = -0.11.

p(x>68), the z-score formula is (68-64)/18 = 0.22.

The rest answer are mentioned below with calculation.

It is (X-μ)/σ, where X is the value we are evaluating, μ is the mean of the population, and σ is the standard deviation of the population.

For the first two questions, p(x<62) and p(x>68), we can use the z-score formula to calculate the probability. The z-score formula is (X-μ)/σ, where X is the value we are evaluating, μ is the mean of the population, and σ is the standard deviation of the population.

For the first question, p(x<62), the z-score formula is (62-64)/18 = -0.11. This means that the probability of x being less than 62 is 0.3767 (from the z-score table).

For the second question, p(x>68), the z-score formula is

(68-64)/18 = 0.22.

This means that the probability of x being greater than 68 is 0.5987 (from the z-score table).

For the third question, the probability that a randomly selected pregnancy lasts less than 260 days can be calculated using the z-score formula.

The z-score formula is (260-266)/16 = -0.375. This means that the probability of a randomly selected pregnancy lasting less than 260 days is 0.3296 (from the z-score table).

For the fourth question, the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less can be calculated using the Central Limit Theorem.

Since the sample size is 20, the standard deviation of the sample is

16/√(20) = 4.

The z-score formula is (260-266)/4 = -1.5.

This means that the probability of a random sample of 20 pregnancies having a mean gestation period of 260 days or less is 0.0668 (from the z-score table).

For the fifth question, the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less can be calculated using the Central Limit Theorem.

Since the sample size is 50, the standard deviation of the sample is

16/√(50) = 1.83

The z-score formula is (260-266)/1.8 = -3.3.

This means that the probability of a random sample of 50 pregnancies having a mean gestation period of 260 days or less is 0.0062 (from the z-score table).

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Answer

Age of Car in years is represented as x

Avg. Miles per Gallon is represented as y

y = 0.97x + 1.214

Correlation Coefficient = 0.673

Explanation

Age of Car in years is represented as x

Avg. Miles per Gallon is represented as y

The datapoints are fed into a calculator and plotted with the datapoints also processed according to some formulas that'll be provided here

The first figure contains the data points and the regression data processed to be used to calaculate the required parameters.

The second attached image shows the plotted data and the line of best fit and the equation that best represents the relationship between the two parameters.

Then the last image shows the parameters used to calculate the equation of correlation and the correlation coefficient.

Hope this Helps!!!

Answer:

67

Step-by-step explanation:

d(n) = 4n + 2

= 4(5) + 2

=22

t(d(n)) = 3(22) + 1

= 67

Explanation:

Given the function:

5y = 2x - 10

Choose points for x, such as -2, -1, 0, 1, and 2

Solve for the corresponding of each point of x for y

For x = -2

5y = 2(-2) - 10

5y = -4 - 10

5y = -14

y = -14/5 = -2.8

For x = -1

5y = 2(-1) - 10

5y = -2 - 10

5y = -12

y = -12/5 = -2.4

For x = 0

5y = 2(0) - 10

5y = 0 - 10

5y = -10

y = -10/5 = -2

For x = 1

5y = 2(1) - 10

5y = 2 - 10

5y = -8

y = -8/5 = -1.6

For x = 2

5y = 2(2) - 10

5y = 4 - 10

5y = -6

y = -6/5 = -1.2

Inputs (x): -2, -1, 0, 1, 2

Outputs (y): -2.8, -2.4, -2.0, -1.6, -1.2

The graph of this equation is shown below:

Answer:

Step-by-step explanation:

Expresión x--12.5*y-612*x-3*y-2 = 9.5*y-611.0*x-2.0

The misleading about the data shown on the figure is the clas width

From the question, we have the following parameters that can be used in our computation:

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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Answer:

Answer is 2

Step-by-step explanation:

To get rid of the fraction:

5*4x-5 =3

5

4x-5=3

4x=3+5

4x=8

x=2

Step-by-step explanation:

It should be 5x4= 20

-5=15

15÷5

=3

Answer:

b = (A - 3C)/2

Step-by-step explanation:

2b = A - 3C

b = (A - 3C)/2

Answer:I am adding the brackets to show in which order the expressions will be evaluated:

A.

(4 ÷ 4) + 4 – 4 = 1+4-4 = 1 (the correct answer)

B.

(4 · 4) – (4 ÷ 4)= 16-1 = 15

C.

4 –( 4 ÷ 4) – 4= 4-1-4 = -1

D.

(4 ÷ 4) + 4 + 4 = 1+4+4 =9

hope this help yu the answer is A

hope this hlpe

Step-by-step explanation:

Answer/Step-by-step explanation:

a. Volume of hemisphere = ½(⁴/3πr³)

r = 30 cm

Volume = ½(⁴/3 × π × 30³)

Volume = ⅔ × π × 27,000 = 56,548.6677 ≈ 56,549 cm³

b. 4,500 cm³ = 1 min

56,549 cm³ = (56,549 × 1)/4,500

= 12.5664444 ≈ 12.6 mins

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:

The answer is 56°. Angle B is an exterior angle of triangle ABC, which means it is equal to the sum of the two remote interior angles (angles A and C). Angle A is 35°, angle C is 121°, so angle B is 56°.

Answer:

$2.48

Step-by-step explanation:

29.75/12 =2.479

To the left five units, up three units describes a translation that would produce triangle A′B′C′ . A polygon with three edges and three vertices is called a triangle.

What is vertices of triangle ?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. ΔABC refers to a triangle with the vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

The definition of the vocabulary used to classify triangles may be found on the first page of Euclid's Elements, which dates back more than two thousand years. In modern classification, names are either directly transliterated from Euclid's Greek or translated from Latin.

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Answer:

a)

slope = (-4 cm) / (650 cm)

slope ≈ -0.00615

b)  the section of the road measured horizontally is approximately 3983.74 cm long.

Step-by-step explanation:

change in horizontal distance = (change in vertical distance) / slope

change in horizontal distance = (-24.5 cm) / (-0.00615)

change in horizontal distance ≈ 3983.74 cm

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

6

Step-by-step explanation:

Answer: 6
The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6.

Multiply weeks by minutes per week:

52 x 205 = 10,660 total minutes per year

Work Shown:

205 minutes: 1 week

52*(205 minutes) : 52*(1 week)

10660 minutes : 52 weeks

10660 minutes : 1 year

Answer:

-7

Step-by-step explanation:

Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).

The linear factors of the given polynomial is (2x+1)(4x+3) and (3x-2).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given function is f(x)=24x³+14x²-11x-6 and one of the factor is (2x+1).

Here, 24x³+14x²-11x-6 can be written as 24x³+12x²+2x²+1x-12x-6

12x²(2x+1)+1x(2x+1)-6(2x+1)

= (2x+1)(12x²+1x-6)

= (2x+1)(12x²+1x-6)

= (2x+1)(12x²+9x-8x-6)

= (2x+1)[3x(4x+3)-2(4x+3)]

= (2x+1)(4x+3)(3x-2)

Therefore, the linear factors of the given polynomial is (2x+1)(4x+3) and (3x-2).

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The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

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Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

The image of the figure after the dilation is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Scale factor = 2 centered at the origin.

The coordinates of the figure are

(2, 2), (2, 5), (-2, 2) and (-2, 5)

When dilated by 2 centered at the origin, we have

Image = Points * 2

Substitute the known values in the above equation, so, we have the following representation

Image = (2, 2), (2, 5), (-2, 2) and (-2, 5) * 2

Evaluate

Image = (4, 4), (4, 10), (-4, 4) and (-4, 10)

The graph is added as an attachment

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Answer: x = -2.

Step-by-step explanation:

-8x + 44 ≥ 60

Subtracting 44 from both sides, we get:

-8x ≥ 16

Dividing both sides by -8 (and reversing the inequality since we are dividing by a negative number), we get:

x ≤ -2

Next:

-4x + 50 < 58

Subtracting 50 from both sides, we get:

-4x < 8

Dividing both sides by -4 (and reversing the inequality), we get:

x > -2

Putting the two inequalities together, we get:

-2 < x ≤ -2

This means that the solution for x is x = -2.

The area of park in terms of scale drawing is 79200 square yards with scale drawing of a rectangular park is 8 inches wide and 11 inches long.

Area of rectangle=Length * width.

Given:

scale length of rectangular park = 11 inch =

scale width of rectangular park = 8 inch

scale length / actual length of park = scale width/ actual width of park

11/330= 8/ actual width of park

1/30 =  8/ actual width of park

actual width of park = 240

So,

Area = length* width

=330*240

= 79200 square yards

Hence, the area of the actual parking is 79200 square yards.

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